Mister Exam

Other calculators

x^3-1
Solving integrals/ x^3-1

Integral of x^3-1 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2            
  /            
 |             
 |  / 3    \   
 |  \x  - 1/ dx
 |             
/              
0
∫02(x3−1) dx\int\limits_{0}^{2} \left(x^{3} - 1\right)\, dx 
Integral(x^3 - 1, (x, 0, 2))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x3 dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

    1. The integral of a constant is the constant times the variable of integration:

      ∫(−1) dx=−x\int \left(-1\right)\, dx = - x

    The result is: x44−x\frac{x^{4}}{4} - x

  2. Add the constant of integration:

    x44−x+constant\frac{x^{4}}{4} - x+ \mathrm{constant}

The answer is:

x44−x+constant\frac{x^{4}}{4} - x+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                        
 |                        4
 | / 3    \              x 
 | \x  - 1/ dx = C - x + --
 |                       4 
/
∫(x3−1) dx=C+x44−x\int \left(x^{3} - 1\right)\, dx = C + \frac{x^{4}}{4} - x
Simplify
The graph
0.02.00.20.40.60.81.01.21.41.61.8-1010
Plot the graph f(x)
The answer [src] 
2
22 
=
= 
2
22 
2
Numerical answer [src] 
2.0
2.0
The graph
Integral of x^3-1 dx

    Use the examples entering the upper and lower limits of integration.

    © Mister Exam – Calculator